Risk

James Hansen recently published analysis showing that temperature has increased enough that the probability of extremes (in particular, extreme heat) is significantly greater than it used to be. This has consequences.

We have indeed witnessed a spate of extreme heat events recently: the 2003 European heat wave, the monster Russian heat wave of 2010, Texas/Oklahoma 2011, and this year’s heat/drought in the USA. Hansen emphasized that these extreme events are so much more common that such a concordance simply wouldn’t have happened without global warming. Extremes are 10 times more likely than they used to be. We would of course have heat waves anyway, but global warming has made them distressingly more frequent.

Cliff Mass expressed another viewpoint. He suggested that the net temperature increase is small compared to the extremety of the observed heat waves, so global warming is only responsible for a small fraction of the heat. Therefore, he suggests, global warming has had little impact on heat-related stress on humanity. We have heat waves anyway, global warming has only made them a little worse.

I think that a proper evaluation should emphasize the risk of extreme heat (or general extremes). Risk is sometimes defined as the product of probability times cost. I’ll explore what that would be in an extremely simple model of the impact of changing temperature. This is just an exercise to explore the impact of making extremes both more extreme and more common, and the model I’ll apply is simple — in the extreme. But, you’ve got to crawl before you walk.

Here’s the model. Temperature (which could represent temperature on any time scale you choose, but should not be longer than seasonal or annual averages) is a random variable which during some reference period is governed by the normal probability density f(x). We’ll be interested in the temperature in some region and its cost, or damage, to that specific region. We’ll measure temperature in standard deviations above or below the mean during the reference period (which we will take to be a time of minimum risk), so our probability function is the “standard” normal with mean zero and standard deviation one:

Because global warming will change that distribution, we’ll need to use the full form of the normal pdf, namely

,

where is the mean (which starts at zero) and is the standard deviation (which starts at one).

We’ll say that the damage due to climate is a function D(x) of that temperature. During the reference period, we’ll suppose that the damage is zero unless temperature is at least two standard deviations above or below the mean. Beyond those extremes, it will increase slowly at first, but by the time temperature reaches 10 standard deviations (either high or low) we’ll consider damage to be total. I used this damage function, which is zero up to +2 std.devs, follows a sinusoidal curve to 10 std.devs, and remains total (damage=1) beyond that, with the damage function for negative temperature being a mirror-image of that for positive temperature:

Finally, we’ll define the risk as the expected value of the damage. This is

,

where the integration limits are from minus to plus infinity.

For convenience, I’ll define a standard normal variable

,

so that

.

Then our risk integral can be written as

.

Now let’s look at how the risk changes when the mean and standard deviation change. If we simply increase the mean while holding the standard deviation constant, the risk changes dramatically. Here’s the ratio of the risk at a variety of mean temperatures to the risk when the mean is zero (the risk ratio):

Note that even modest temperature increase, a single standard deviation, increases risk substantially. At one standard deviation, risk increases by a factor of 6.5. That is indeed a sizeable increase, and argues very strongly that Hansen’s perspective is a realistic viewpoint of the impact of global warming, while Mass’s perspective is not.

Perhaps more disturbing, as the mean continues to increase risk increases ever faster. When the increase reaches two standard deviations, risk has been magnified by a factor of more than 40. If climate-related damage is 40 times greater, then suggesting that 2 standard deviations is a small fraction of the size of a massive heat wave is shown to be a fundamentally faulty perspective.

Here’s the impact of increasing the standard deviation while holding the mean constant:

Again, significant changes in standard deviation lead to large changes in risk. I will mention that for this constant-mean case, half of the risk involves the likelihood of extreme cold events.

You’re probably wondering about the combined effect of increasing mean and standard deviation.

Note that the graph shows the logarithm (base 10) of the risk ratio. Increasing either mean or standard deviation leads to large risk magnification, increasing both together amplifies the effect.

Of course this model is an oversimplification. But I think it does demonstrate the main point, that Cliff Mass’s perspective is fundamentally flawed because it fails to account for the dramatic increase in the frequency of extreme events. It also illustrates that as warming progresses, risk increases much more rapidly. We’ve already experienced “1 sigma” of warming, and paid the price. The consequences of the next sigma will be devastatingly greater.

This much is certain: dealing with climate change is not a game. I don’t think we can afford the risk.

90 responses to “Risk”

Hi Tamino,
Two comments.
1. As you say, there is already damage visible at 1 standard deviation of temp. There are texts out there that state that agriculture ‘as we know it’, and hence human civilization, will disappear when the temperature average increases with 3 or 4°C, or about 5 s.d. What would happen if you have D go from 0 to 1 in the interval [0.5sd, 5sd], instead of [2sd, 10sd] illustrated in the text?

2. 2°C increase seems much more than 2sd, hence an unacceptable risk. So this means that all talk of limiting growth to double CO2 or 2°C or similar leads to unacceptable risk. Hence we’ll need to define a new policy.

….
Professor Watson is among the most respected scientists in the world on climate change policy.
…
“I wouldn’t rule out a 5 degree world and that would be quite serious for the people of the world especially the poorest.”

+5K would be “Quite serious … especially for the poorest.”

Is that all a leading expert can muster? He must not have read _Just Six Degrees_ nor Hansen nor Tamino.
How can the message be spread? Does anyone have contact with this “expert”?

In Kansas in places this year, corn wasn’t simply stunted or failed to prosper and mature due to drought. The corn died on the stalk due to temperatures over 112F.The area was small this time. As we warm, the area will expand and the length of the exposure will increase.

We’ve had .8C of warming so far. When he get 1.6C sometime in the middle of the century. we will regularly face the extermination of the crop that’s in the fields. Meanwhile, population is expected to continue to grow. Fertilizer is going to become far more expensive. (We passed Peak Oil ~2007. ). That’s the set up.

It’s beyond bizarre that the governments of the world (and particularly ours in the US) aren’t doing anything at all to help address these imminent risks. (Some %@#@!s in office are even denying AGW exists! Words have literally failed.)

A bunch of us who were avid gamers in our youth developed our own rules for Risk, because we thought the original rules were too tame/subject to luck. In our version, luck played a role, for sure. But strategy eventually won the day. I wish I could remember exactly what we changed, but it was so long ago…

I am trying to pinpoint the Martin Weitzman paper that discusses the theoretical case where the damages are rising meaningfully faster than the probability of those damages occurring. It’s not strictly on point, and it’s not exactly rocket surgery, but germane nonetheless, I think.

The best I have come up with is this, but I think there is another, better discussion. Still poking around. This one appears to be describing damages as a function of GHG concentrations as opposed to temps… Anyhoo… here is an excerpt:“This paper investigates what might happen to an economic analysis of climate change with a significantly more reactive damages function than the quadratic and with PDFs having tails of varying degrees of fatness. The paper attempts to give some extremely rough ballpark estimates of the differences in steady-state temperature PDFs and damages as a function of greenhouse gas (GHG) target concentration levels. These differences vary greatly according to the specification, but on the whole they are substantial enough to suggest that in some situations – especially when catastrophic damages interact with fat-tailed uncertainty – we might be underestimating welfare losses considerably. The critical question here is: How fast does the probability of a catastrophe decline relative to the welfare impact of the catastrophe? Even tiny probabilities can be offset by negative welfare impacts that are big enough. In such conditions the fact that the tiny probabilities are themselves unknown is, other things being equal, more troubling than if they were known precisely. With the examples being considered in this paper, the primary reason for keeping target GHG levels down is to insure against high-temperature catastrophic climate risks. In situations where fat-tailed PDFs are combined with a reactive damages function, the welfare di¤erences between various target GHG levels are typically very large and there is a much stronger case for keeping down GHG target levels than when tails are thin or damages are quadratic.”

Tamino, I think this is a rare case in which you’ve overstated your case. The risk ratio depends critically on the on the shape of the damage function. In particular, it is strongly affected by the assumption that there is no damage within 2 standard deviations of 0. Divide anything by zero and you get a big number. If “We’ve already experienced ‘1 sigma’ of warming,” we should have seen a factor of 6.5 increase in damage. If we have seen that much increase, I missed it. The Munich Re plot you showed on August 22nd makes it look more like a factor of 2-3. …and that’s raw data which needs some inspection (with better communications than 30 years ago and about twice as many people in the world, some events that were “non-catastrophic” may now be considered catastrophic.)

[Response: Indeed the risk depends on the form of the damage function. As I said, this is just an initial exploratory analysis, and I’d say the given choice is not an unreasonable first step. I may investigate other choices since I think it’s a very interesting subject and is deserving of more study.

The Munich Re plot is the number of disasters since 1980. Therefore it includes increased frequency but not increased severity, which might make a factor 2-3 become 6.5. As for the general increase in observed disasters and their severity, especially extreme heat waves, I haven’t missed ’em they’ve been rather obvious.

I’d say the main points stand firm. First — that characterizing risk by the size of the increase relative to the size of the extreme value is foolish, it ignores both the facts that frequency increases dramatically and that damage is a highly nonlinear function of the extreme value. Second — that the 2nd standard deviation of temperature increase is gonna be a helluva lot worse than the 1st. When we get to 3 standard deviations … I don’t even want to think about it.]

Jeff T. I am not sure I understand your comment about “dividing by zero”. Even with no temperature change there is still finite probability of >2 sigma fluctuations, and so finite risk. Did you not understand that one must integrate over the temperature range to determine the total risk?

Slightly off topic, but at the bottom of your excellent post, there was an ad on my browser for ‘The Australian’ newspaper, one of the leading purveyors of climate change denial in the Australian media landscape. I assume it was Google or WordPress that put it there, but… had to laugh.

> At one standard deviation, risk increases by a factor of 6.5. That is indeed a sizeable increase, and argues very strongly that Hansen’s perspective is a realistic viewpoint of the impact of global warming, while Mass’s perspective is not.

I don’t think you can say that – the key unsupported word is “realistic”.

You’ve made no attempt to justify the realism of your damage profile. Unless you can do that, your results are purely illustrative.

Also, you’ve assumed that the current climate in your model is optimal (in terms of mean at least). Fairly clearly in the real world that isn’t true, at least locally. Reflecting that, I think that the damage function (in Stern, for example) for small warming is negative.

[Response: Of course it’s just illustrative. I thought I made that clear, but apparently I failed.

What it illustrates is that if you don’t account for the increased frequency of extremes and the nonlinear increase of damage with severity of extremes, you can’t properly estimate risk. That’s the main point. It seems to me to be one of Hansen’s central themes, which makes his perspective realistic, but is ignored by Cliff Mass, making his perspective unrealistic.

As for the risk from 1 standard deviation increase, I think the observed impact on agriculture and animal husbandry in the U.S. these last two years and in Russia in 2010, and the increase in weather-related disasters which is of such concern to the insurance industry, support the claim that risk has already increased. Whether it’s as much as 6.5 times greater of course I don’t know. I would add, with high confidence, that the next standard deviation will be a lot worse.]

William, I don’t think you are comprehending the risk paradigm. I think that Tamino’s cost function is actually fairly generous–it gives us a free pass out to 2 sigma events. If your point is that even for the -2 sigma to + 2 sigma region cost is nonzero, fair enough. However, the bulk of the damage will still occur for events in the tail, and while the numbers might change, the overall message would not.

If it is your contention that the damage/cost function should slope downward from -2 to +2 sigma, I would say that this is inconsistent with what data we have. Moreover, any slope would have to be shallow, and risk would still be dominated by events out in the tail.

If it is your contention that the cost/damage function rises too rapidly in the extremes, I would also say that you don’t have a leg to stand on. Not only are extreme events more damaging inherently, they are also much harder to mitigate.

I have played around with similar schemes in my day job. Tamino’s cost/damage function represents a “mean” cost for an m sigma event. Of course, not all such events will have the same cost. A 5 sigma drought in northern Siberia will not have the same consequences as one in the US breadbasket. One can capture this by representing the cost/damage “function” as a series of distributions for each value on your probability scale. One can also choose, say, a 90% upper limit for damages.

However, no matter how you vary the analysis, you find that you are dominated by the extrema, so Tamino’s analysis is quite illustrative and more than fair to Cliff Mass. The only way you could be right is if your damage/cost function was strongly negative for warmer events out to 2-3 sigma–and if you contend that, you are delusional.

Good piece, but as most simple models, it understates the risk. It assumes a normal PDF for temperature, and it assumes cost/impact is linear.
However, temperature in the context of a drought is not linear. As the temperature rises, the humidity goes down, and then when it is hot, the temperature rises faster.
And, impacts are not linear. As Jeffrey Davis point out above, most crops, such as corn have very particular limits as the temperatures that they tolerate. The crop does well up to the critical temperature, and then a fraction of a degree more and yields decline. Another fraction of a degree warmer and the crop fails. This does not have to be some average; 10 days of warm nights during tasseling will ruin a corn crop. This year’s sour cherry crop was spoiled by a bit of warm weather early in the spring that caused the trees to bloom too early in the spring.
Then, we have the effect of drought on crops where the temperature and lack of moisture combine to damage or destroy the crop.
Since 2007, we have had enough weather related crop losses to dramatically raise the global price of food. See for example http://www.fao.org/fileadmin/templates/worldfood/images/home_graph_3.jpg
Since 2007, there have been 6 consecutive exceptional Arctic sea ice melt events. When we have the same weather in the same region in the same season in 6 consecutive years, that weather is “climate”. When CO2 was 350 ppm, the Arctic did not melt. When CO2 is above 390 ppm the Arctic sea ice melts every year. And that sea ice melt changes the Arctic from a desert into an ocean. That changes global atmospheric circulation. That changes when, where, and what agriculture can produce.

Not “will change”, but ” AGW is rapidly changing when, where, and what agriculture can produce. And this has costs and impacts now.

I am sure you have already thought of this, but this blog post seems conceptually as important as the post that eventually became “Global temperature evolution 1979-2010” in ERL. So, I hope you get it published once you are done tinkering with it.

[Response: I agree that it’s conceptually very important. But honestly I don’t think I have the expertise to give the subject the treatment it deserves. It is interesting enough that I do plan to tinker with it plenty. Who knows?]

This is problematic issue in the sense that with some plausible adjustments in the assumptions one can obtain almost any result. Therefore one cannot really learn much without rather solid knowledge on the proper input.

As it is I would say that we have just a restatement of the precautionary principle. The precautionary principle is valid but it’s extremely prone to misuse because conclusions based on it are so sensitive to some difficult-to-justify assumptions.

I gave above the reference to a paper by Nordhaus where he discussed earlier work of Weitzman. Weitzman’s argument was written in the same spirit as this post. Weitzman looked at the possible damages and chose certain assumptions for the probability distributions and damage functions. He concluded that the expectation value is infinite (or at least this statement gives the idea of his “dismal theorem”). Nordhaus went trough the analysis and concluded that the assumptions of Weitzman are unlikely be valid and that with more reasonable assumptions the result changes: we do not have the infinity, but Nordhaus’ analysis doesn’t really tell whether the damage could be very large while being finite.

Looking at the assumptions of Weitzman my own conclusion is that he misinterpreted severely the estimates of climate sensitivity that he used as one principal input. That was not essential for the scientific conclusions which were actually not dependent on that input but that data had a major influence on some comments concerning the practical importance of the analysis.

I wrote the above just as an example on how considerations of the type presented in this post have led to totally contradictory conclusions among two of the best known names of environmental economics. That the best environmental economists cannot always reach conclusions that are quantitatively in the same ballpark or even qualitatively similar is an unfortunate fact. While most if not all of them agree that climate change is a serious concern they may have very different views on which practical approaches are wise. All might agree on the positive value of some weak actions but trying to find agreement on something concrete that would be strong enough to really make an effect on the CO2 level may be an futile attempt. There are risks not only in the consequences of the warming but also in the unwanted side effects of the actions.

Global warming is not the only major problem and concentrating on that over all the others may well be detrimental for the human well-being. For this reason it’s important to have better estimates of the certainty of the strength of warming and on its consequences. Only more quantitative knowledge allows for proper comparison of conflicting interests. When we are considering big global effects we cannot afford an approach based on wishful thinking.

Pekka,
I disagree. Play around with your loss function. As long as you do not make it unreasonably forgivng on either side of zero, you will find shifts raise losses dramatically. And we do have data to constrain it. For instance, we know that as temperature rises, GDP growth falls on average.
And nobody is advocating ignoring other risks. Indeed, one risk we must face is replacing our outmoded and soon to be worthless fossil-fuel based energy infrastructure.

And it seems to me that ignoring risk is wishful thinking of the worst kind.

I’m sorry, but I cannot find in your comment anything that has any connection to what I wrote. I cannot believe that by writing is so badly written that it would be impossible to understand better what’s about.

Pekka,
First, your contention that “plausible adjustments” could be made to yield any desired result is simply false. The conclusion that risk increases dramatically is robust over prety much any loss function you care to use unless you make the very improbable assumption that events out to >+2-3 sigma are actually beneficial compared to those on the negative side.

Second, your contention that anyone is suggesting we concentrate on climate change to the exclusion of all other threats is a strawman.

Let’s answer the easier part first. I used the words “wishful thinking” at the end of my comment in a paragraph where I discussed the fact that there are other major problems and that we are considering development where really major changes are searched for. In this connection I had in mind that very many people are willing to bet heavily on some particular choices. The real consequences of any of strong actions are not known and what I consider wishful thinking is to make some particular choices in spite of this lack of knowledge.

That paragraph did not refer particularly to what Tamino presented in his post. I have also noticed that he presented the calculation as an example of the effect, not as a quantitative analysis of the actual situation.

Concerning the plausible choices of assumptions my own view is, indeed, that there’s enough freedom for getting almost any results. Playing with rapidly changing probabilities and cost functions allows for that. Of course each of us as his own views on “plausible”.

Clicking my name you get to my own pages where I started to discuss these issues. Unfortunately I couldn’t keep up with my wishful thinking on what I’m able to write, both because going forward started to get really difficult and perhaps also laziness as the work needed for next substantial contribution started increase post after post.

jcbmack, doubtless the point of your physical examples is to show that the risk from climate change may be much greater than Tamino supposes, but the relevance is not clear. How do your examples relate to the consequences for us of increasing the planet’s mean temperature?

My points are that we do not know what risks there are or how to know them. Heat flow Q is a process that transfers energy and is a path function while T is a state function measuring average kinetic energy. Heat is not a substance itself and in accordance with the 2nd law of Thermodynamics heat flow or transfer if you prefer cools objects/surfaces/gases as it moves to warm others always from a hot source to a cold sink and never in reverse. W is also a path function and not a state function and it is related to Q. Air conditioners and refrigerators use compressors to perform work against a temperature gradient but not in the same manner that greenhouse gases perform work or the external energy of the sun does.

A z score and a standard error can tell us if a given value or score is above, below an average, or how far it maybe. I am not seeing any data to support such a use and the placement of the symbols within these equations are not in any standard used scientific or statistical implementation. Is this a new equation?

Integrals (anti derivatives) measure the sums of rate of changes over a given time period using the rectangles under the curve and derivatives measure rate of change at specific points on a curve, but how and why and what are we measuring here in these equations without corresponding graphs?

Finally, what is meant here by negative temperature because in physics and Chemistry, I learned this about it:

I am not at this point saying anything one way or the other. I am asking about this thread, these equations, the data this is based upon explicitly, (I saw Hansen mentioned, but am unsure if the equations were derived from Hansen or not) the reasons for the order of the given equation and so forth.

In calculus I,II,III and IV I never saw these equations in their totality, ever, and in statistics I never saw them either. I have seen these symbols used in other equations, but how exactly are these derived and used?

The links I left illustrate how difficult it is to calculate heat flow and see temperature gradients in very small systems. Even with a central tendency of weather known as climate, there is a huge planet to sample, large margins of error, CI’s not yet well established, and chaotic activity within climate too.

Again I am not taking any position in this post. None. 0. I have taken positions on both sides and in the middle before. Here I can just ask and illustrate the complexity because of my training and experience with heat flow, temperature gradients and math in general among other things. My tone is neutral too. If Hansen’s data is necessary to understand this where exactly is it most useful and where can I see the work put in to produce these equations and the visual aids?

Please, fellow posters do not point me to another blog. I read all of the climate blogs when I have downtime from work. I know RC, Skeptical Science, Tamino’s archived posts too. I see equations Tamino has used that I do recognize whether we see the same data or not, but here this is very different.

At some point it is always worthwhile leaving the office and understanding the real world.

One can do extraordinary things with statistics and equations, and in my scientific career I have been repeatedly astonished and delighted at the power of numbers, but there comes a time when practical experience is as important – if not moreimportant – an indicator as might be any numbers on a page.

Talk to any ecologist who understands the relationships with climate had by the organisms s/he studies. They will almost inevitably describe to you, without recourse to pages of calculation, the effect that changes in climate will bring. As would any experienced and competent agronomist. And as much as many humans seem to imagine otherwise, we are slaves to our utter dependence on the global ecology, and to the primary productivity we draw from it.

Ecologists, agronomists, and similarly-experienced people know well the risks: they know them intimately.

Hanging-wringing over equations would be most usefully advanced by placing a violin in said appendage. At least that way we could enjoy a nice fiddle tune as Rome burns.

Jcbmack,
What Tamino has written is pretty straightforward risk analysis. If you have a threat T, which has a probability P(T) of occurring and will cost/cause damage of (C(T) if it occurs, then the risk
R(T)=P(T)xC(T)

The Threat Tamino is addressing could be an extreme heat wave… The probability distribution for the threat is a Gaussian, initially centered on z=0. The Cost function represents the damage due to the event. Now the temperature shifts toward positive values. This shifts the entire Gaussian to the right. The cost function stays the same. That is the analysis.

It is utterly straightforward. Any probability function will look Gaussian if we aren’t too far into the extremes, and the results are robust for any reasonable cost function.

snarkrates the cost function I know from Computer science, economics, statistics, and physics look very different than this and take into account many more parameters.

The other issue is you will not have a Gaussian curve when extending to longer time periods which you really need to really analyze, but do to that you need non parametric statistics and far more data since you are not using a normal distribution. The issues becomes real clear when you need to agree upon and standardize what data you are using, and how you are considering climate sensitivity and why.

Now in addition, you need to perform causal inference using counter factuals like so:

Of course calculus and algebra measuring continuous values like temperature are important. Some calculus can be converted from partial differential equations and integrals to algebra, but not in the same nice way we can for say electronic circuits going from Maxwell’s equations to abstracted formulas.

Thus, what is the straightforward abstraction here from what more complex math and from what data?

jcbmack, OK, now you’re just pudknocking. You clearly have NO idea what you are talking about and are just reading random pages from Google. What you are saying makes zero sense and has no self-consistency. You forget–some of us do this in our frigging day jobs.

[Response: You haven’t given any reason that it’s not useful, other than perhaps that you don’t understand what’s going on. Snark is right, the approach (but perhaps not the cost function) is quite standard stuff and your questions simply made no sense at all.}

“Global warming is not the only major problem . . .”
When I was a risk manager at a major engineering firm, I kept a list of the 300 things most likely to go wrong at a major infrastructure project where we posted bonds to back warranties stretching out for very long time periods.
Now global warming is the only item on the list. It got here before the “the big Earth Quake”. It affects everyone, not just the folks sitting on one plate boundary. And, bottom line ends up being food, so it is of the utmost importance to everyone – whether they know it or not.
So Global Warming may not be the only major problem, but it is orders of magnitude more important than any other problem. And, it is very likely contributing to many of the issues that would appear on a longer list of problems.

You both picked out my sentence “Global warming is not the only major problem . . .”.

The attitudes concerning the uniqueness of global warming as a threat is are certainly essential for the argument.

You and many others seem to believe that global warming is, indeed, totally unique. You perhaps think that it’s genuinely existential and may lead to near total destruction of the ecosystem and near to the extinction of the human race. That’s at least what I read in your messages.

I do consider global warming a really major concern but not so existential that everything else could be put aside. A put also more emphasis on adaptability of both the nature and the human societies. Rapid warming is certainly seriously disruptive but hardly existential taking adaptability into account.

I understand very well that bringing up the other concerns is commonly seen as an excuse for not acting, but there’s more in that. The problem is that having a strong belief that stopping global warming is the ultimate priority does not tell what should be done. To stop global warming some concrete actions must be chosen and the actions must be taken on a level that affects our well-being in many ways. That’s true even, if we really know the consequences of the actions. Even then we may notice that some compromises must be made to avoid even worse outcomes due to the side effects.

Unfortunately the situation is even worse: We do not know any concrete ways of stopping the global warming, We do not know how much any strong concrete actions will ultimately help in slowing down the warming and we do not know the unwanted other consequences of these actions are.

There are certainly things that each individual may do and there are often possibilities to choose between a better and worse alternative without too much risk of erring, but these things are not likely to lead to much change in warming. There are also policy decisions that are technically easy to make like implementing a carbon tax.

A modest carbon tax is also a rather safe choice as it’s almost certain to produce some reduction in CO2 emissions with few side effects, but a modest carbon tax is not effective in stopping the warming. A very high carbon tax is not at all guaranteed to have a net positive value when both its influence on warming and its other effects are taken into account. It’s not guaranteed to be an effective choice in influencing warming in long term. Setting a tax is not a concrete action by itself, it’s hoped that it’s a good incentive for helpful concrete actions but one well known law of economy is that people do not react to incentives exactly as the are supposed to do. That’s a really major risk when nobody knows what are concrete actions that give the right benefits. In such cases the end up in searching all kind of tricks for taking advantage from the incentives without necessarily contributing much to the ultimate goals.

This is again a place to eplain what I had in mind when writing “wishful thinking”. I meant belief that some particular pet decision is both effective and has a positive net value when its real consequences are not known at all.

To make my concerns more specific: Very strong incentives may lead to excessively wasteful renewable energy projects as the technologies are not ready for really wide scale deployment. They may lead to decisions on biofuel production in ways that damage the environment and that cut food production, etc., etc. Trying to be very effective has many features of creating a panic in a theater full of people: When a fire breaks out everybody tries to get out trough the small doors and far fewer are successful than in an orderly exit.

Pekka Pirilä,
So what you’re saying is that AGW will not be too bad because we can adapt but we cannot adapt a priori without screwing up because we’re too dumb to have thought out how to achieve what needs to be done.

But what I find most reassuring in your comment is that you consider “seriously disruptive” AGW will be “hardily existential.” That’s fantastic news! Could you be perhaps clearer on what exactly it is you consider has its continued existance assured? The world population of humanity? A sub-set there of? The world economy? The present political world order? A nation state or two? Or perhaps you consider humanity’s continued existance to be within more flexible smaller cooperative units?

PP: Very strong incentives may lead to excessively wasteful renewable energy projects as the technologies are not ready for really wide scale deployment.

BPL: That would come as a surprise to Portugal, which is getting 45% of its electricity from renewables right now, or Indonesia, which gets 18% of all its energy from geothermal, or Iceland, or Germany, or Spain…

We get also a lot from renewables in Finland. 28% of all energy was renewable in 2011, mostly based on wood and almost all the rest conventional hydro. Some countries like Norway have very much conventional hydro, which makes the share of renewables really high.

Conventional hydro is often low cost and seldom needs any subsidies. In case of Finland also the wood based energy is mostly but not in total profitable without subsidies. (It’s used most widely by forest industry where its costs are low.)

Not all renewable requires heavy subsidies and some of the present production is really far from economic as the subsidies may pay up to 90% of the cost. That’s not far from the situation for the German solar energy although the cost is not anymore quite so high.

Some forms of renewable are either economic without any subsidies or so close to that that modest subsidies or a modest carbon tax on fossil energy are a sufficient incentive. That’s, however, not true widely enough. There are many very significant obstacles that make a sufficiently wide scale renewable energy production a very demanding goal. The severity of the obstacles is the reason for my pessimism on their potential on near or medium term.

More relevant to the arguments that I have presented here is that trying to speed up the deployment of renewable technologies too strongly does not seem to be the approach that gives the best results in long term. A crash program based on very strong incentives is almost certain to lead to a excessively high share of failing projects like power plants that produce very little and will be dismantled before they have produced more than a very small fraction of what would be needed to cover the costs. Even outright fraud will increase rapidly when the economic incentives are very high.

I’m an ecologist. I understand how climate impacts species, and ecosystems.

And I don’t :”believe” that human-caused climate change is “unique” no matter how much you would like to put words in my mouth. I do know that it is a problem that, if left unaddressed, will render insignificant any other problem that humans have created. Except to the extent that it exacerbates these other problems.

The rest of your waffle is just that, and not worth wiping my backside with.

We want to quantify the increased risk of extreme events. One the one side we have people who say that warming wont matter much because 1 degree warming is only a small fraction of a 5 degree heatwave (Cliff Mass & M. Hoerling). As this post illustrates, then this approach is obviously bollocks because it ignores the non-linearity of the cost function. If anything should be considered wishful thinking then it is this type of simplistic view of risk.

Some of you are arguing over what the exact shape of the cost function should be. Yes it is hard to quantify but it is obviously not going to be linear. If you cannot quantify the cost function then you cannot calculate the risk. However, you can atleast look at changes in the return period of crossing extreme thresholds. We know enough to be able to say they cost alot, and we should care whether these extreme events become more frequent. That is what Hansen et al. and Coumou & Rahmstorf looks at. That is clearly the sensible way to do it.

Pekka, thanks for spelling out your concerns more fully. I don’t find your thoughts to be “total crap,” but I do feel that the danger right now is distinctly on the other side–in terms of your analogy, the theatre is burning. An orderly exit is required, but we can’t take time now to create the optimal traffic plan via the most sophisticated analysis. We must find a balance between planning reasonably well, and acting decisively. Paraphrasing General Patton, “A good plan, executed right now, is better than a perfect plan next week (read “decade.”)”

I don’t mean that there were not many things that can be initiated rapidly, but I have great doubts on the availability of policy choices that would be really effective and without other risks comparable to their effectiveness in solving problems due to warming.

As an example I do support a modest carbon tax, but I don’t support a very high carbon tax. By modest I mean something of the order of $20/ton(CO2), but not anything approaching $100/ton(CO2). I don’t think that the tax of $20 would be effective, but I do think that the tax of $100 would lead to many unintended negative consequences and would actually not be very effective either in stopping warming (unless that would be realized through a severe depression, which is not a likely outcome at that level but not totally excluded).

The revenue-neutral carbon tax in my province (British Columbia) is $35/tonne. It’s enough to change my behaviour regarding driving and heating my home. It could be higher and I would be happy. This opinion from someone with a middle class income. The key to not killing the economy is to announce and apply a schedule of increases over a number of years and to return the money collected by reducing other taxes.

In my view, resistance to making polluters pay, be they individuals, families, or corporations, is irresponsible.

Well, Pekka, I would say that we should, if given the two choices you propose, take the $100 tax. According to you, it *may* be effective. The downside (however unlikely) would be a major depression, which is less bad (IMO) than the kinds of warming for which we seem to be setting ourselves up. (If nothing else, the depression would surely be much the shorter event of the two, and would not affect other portions of the biosphere.)

I’ve only read about a few theater fires. In most cases the initial reaction to the fire was to stay calm and sit in place and watch the show while the fire was to be put out. It’s not until some time after the initial discovery of fire that mayhem breaks out and people start trampling one another.

So in reality, the problem with theater fires is non-alarmism, not alarmism. That’s why fire marshals now insist on alarms. Because some idiot was always yelling out, “Hey, no problem. Everybody watch the show. The fire is part of it.”

Might Horatio suggest that next time you do a post like this, you include a phrase like “This is just an exercise to explore the impact of making extremes both more extreme and more common, and the model I’ll apply is simple — in the extreme” (or something to that effect) just so people know what the purpose is and can direct their comments accordingly.

Pekka, I’m afraid I have to agree with Tamino. There are a broad range of things we can do that will improve things and buy time–not just at the individual level, but at the policy level.

For instance, forget a carbon tax. How about to start with we remove the subsidies to Oil, Coal and Natural Gas producers. And if we do set a tax on carbon, how about we do in at a level that is commensurate with the damage done by fossil fuels–from extraction throught refining and transprot all the way to the damage we anticipate arising from greenhouse gasses.

Your argument also seems to ignore the fact that you, yourself are proposing strategies–namely wait and adapt. That is NOT a passive option. Adaptation is wonderful, but how do you propose we “adapt” to the loss of the US Midwest to cultivation of wheat, corn and soy? Move north? There’s that small problem that most crops don’t grow too well on bedrock that was left in Canada when the Glaciers scraped off the topsoil. And how do you propose we adapt when drought closes the Missisippi or the Rhine river to navigation 4 months a year? And how do you propose that we adapt when West Nile virus is endemic 12 months a year, rather than 4.

It is well and good to say, “Adapt”. However, adaptation requires a strategy every bit as much if not more than does changing our energy infrastructure. And the thing is that both will be essential to the survival of civilization, because we have simply waited too damned long to avoid serious consequences from climate change.

Here’s the thing that makes global climate change unique, Pekka: IT IS GLOBAL. It changes the conditions that have persisted for roughly 10000 years–coincidentally the period during which all the infrastructue on which our modern civilization depends was developed. Frankly, I don’t think it was a coincidence.

Do you seriously claim that we have subsidies for oil, gas and coal at a level that removing them would be a significant part of an effective solutions? Subsidies in the sense of the word it has mostly been used are not that widespread or large. If you think about subsidies in the sense of not paying for externalities then the carbon tax is just a way to cancel such subsidies.

The requirements for reaching goals like halving the carbon emissions or going even to 20% as is commonly proposed require actions at a totally different scale. Several countries including Germany and UK have declared their willingness to proceed along lines that are supposed to produce these kind of results but I cannot see how they could succeed in reality. The future will tell, but I’m not the only one who is highly skeptical.

Al and Snark, it too use statistics and various forms of math along with algorithms to organize data to make assessments. Stating that you do those stuff without any answer of substance is not an answering my query. I asked honest questions but received no answers. Scary, actually your vague and hostile answers.

jcbmack,
Yep! Them there answers were hostile. But this is not to say such a situation is insuperable. There may be language barriers to negotiate (which appears to me there is) but … if you want to ask an honest question (or two) and get an honest answer, ask it (them). Don’t give us bullshit lectures on subjects you patently have no competance in!!!

You cannot just say the cost function might not be applicable but state the equation is standard. How and why is it standard? I understand risk assessment, and this is not even close to adequate as it stands. I have seen other posts of yours Tamino where, we may not agree on the conclusions but the equations were fine and the symbols were in proper order. I would add definitely the cost function as shown here is no useful.

I will not get into the views on each side as that detracts from what I am asking here, but I do mention it as I am not trying to troll or derail the thread. I have already demonstrated applicable math and science skills, but can do again if needed. The point is you cannot get information here as is. If you were to show me solid equations based upon solid statistical laws and rules, with the proper order of symbols, notation, based upon a data set showing temperature based risks, even if I said to myself, this data is not robust enough, or I personally do not believe this, I would have the decency to say in a post on your blog, great work with the math based analysis of a given data set. Even knowing I have changed my views several times over a 5 year time span, based upon data, I would be man enough to do that. I have done so in the past Tamino–and would certainly do it again. Maybe you have been very busy–I have some down time now so it is easier for me to look at the holes in arguments and calculations… here, however, this is not what I usually see from you in terms of effort.

My last post above this one, too is wrought with typos… what is good for the goose is good for the gander:) I certainly make mistakes too of all sorts. This is not one of them.

[Response: You’re being absurd. The stuff about “proper order of symbols, notation” convinces everyone (including me) that you really haven’t a clue — and NO, we do not want you to demonstrate math skills. You call the cost function “not useful” but give neither evidence nor logic. And you might attend to this comment.

From everything you’ve said I conclude that it’s not worthwhile to discuss the issue with you. So I’m not going to. If by some miracle it turns out I’ve misjudged the value of your inquiry, I can live with that.]

This (apparent) withdrawal of jcbmack does leave me wondering which of the many unfortunate characteristics of his comments here prevent(ed) me from pointing out what the question was that he was trying so so hard to ask.

I think it was the off-handed query about negative temperatures with the reference to the Scott Chase negative absolute temperature machine that was the clincher. It demonstrates such a high level of ignorance/arrogance that any redemption of the situation had to come from him.

PP, I surmise that this sort of thing:“Global warming is not the only major problem and concentrating on that over all the others may well be detrimental for the human well-being.”

is the key to the disagreements several here have with you and other thoughtful inactivists. I suspect that you and Andreas Muenchow (in the previous post) have no concrete explanation of how solar panels or the like will impede the solution to other world problems. Rather, you seem to have some vague forboding concerning any large scale use of non carbon energy, as if it is somehow wrong and great suffering must follow.

“It’s often easier to state what we should not do that what we should do. That’s the real problem.”

No, what to do is clear. The problem is that so many well meaning people like yourself have been induced to balk at doing it.

How did this happen? (*)

“Do you seriously claim that we [USA at least] have subsidies for oil, gas and coal at a level that removing them would be a significant part of an effective solution?”

If you must see lots of numbers, read the endless Unforced Variations thread at Real Climate. But always

Deploy, deploy, deploy.

=======
(*) The expression reminds me of something. It was in Paris. No, Cherbourg, a french town where it rains.
movie – The Umbrellas of Cherbourg iirc (**)
a young man, a young woman and rain. The young woman gets pregnant, leading to a conversation with her mother.

Mother: How did this happen?
Daughter: In the usual way.

PP, is there a usual way for you and people like you? A usual way to become non-carbon phobic, so that you are sure the
manufacture of too many wind turbines and solar panels will lead to great harm somehow? So that you do not see the obvious

answer –
What to do?
Deploy alternate energy (the 14 “wedges”, above) as fast as possible. Of course. What else?
Make the modest, helpful and healthful (links above) changes to incentives that will make the market grow and grow.
Is there a usual way to become unable to see this, and see only danger from too much non carbon energy?

I do think that solar panels are an valuable alternative in many cases, most importantly in places without access to reliable grid. I have spent some time in studying energy alternatives in third world context and agree that solar panels have an important role there both in combination with efficient led lighting and as source of power for other rather low energy devices like mobile phones. Solar panels start gradually to find appropriate applications also in grid connected systems where the insolation is high and peak power demand coincides with the most sunny periods (as it does when the very energy intensive application of air conditioning leads to the highest load).

It’s important to put sizable resources in developing new energy technologies and that requires economic support on significant scale. One way to support development is through incentives for deployment. At some point it’s the most efficient way but in other cases it’s extremely wasteful of both money and intellectual resources. When we are too far from acceptable economics the subsidies do not influence as much the research and development important in long term as the do support some tricks of getting advantage of alternatives very often less likely to be the right ones in long term. More is resources put in mass production of old technologies than in developing new ones. That’s very wasteful if the old technology is too far from competitiveness and the next generation so different that the investments not applicable to that.

The remaining professional duty that I have is to contribute in the development of new energy efficient choices at my old university. Having worked with energy technology research for 30 years has made me to believe that it’s important to search for genuinely new ideas, but to avoid wasting resources on large scale in unlikely solutions. We must all the time search for new but we must also be realistic of what our present knowledge allows for.

I return to the words “wishful thinking” because wishful thinking is behind really many activities that have turned out to be of little real value but that have had disproportionate costs and in some cases also damaged the environment. I’m not against action but I’m against action that’s too unlikely to have a positive net value – and I mean a positive net value taking all consequences into account and among them very importantly the value for further future developments.

I appreciate your courteous and patient reply. I think we are closer to understanding each other. But still –

Your words are replete with vague forboding about large scale use of non carbon energy. For some reason it won’t work, it will backfire, there may be some market inefficiency. Yet you don’t show the same concern regarding the continued use of carbon.
Why not? Your concerns seem directed toward protecting the status quo, even though that is not your direct objective.

All of the 14 methods in the plan I linked (which is only one of several such plans) do in fact work. They provide energy without burning carbon. If you are concerned with the quantities of energy that may be produced by these methods, I again recommend the Unforced Variations thread at Real Climate.
Incentives clearly work. Transfer Carbon’s subsidies to other energy sources and make Carbon pay for some of the environmental
damage it does, not to mention being a factor in mid-east wars, and alternative energy will be in high demand. What about situations where something else is called for? Fine, do something else in those situations.

“But surely we should never invest in solar panels, etc. because next year’s model may be better.” [Not a quote, just a strawman for obvious purposes]
Having a new model every year is industry’s preferred overall model. The large scale manufacture of the next model is finaced by the sales of this year’s model.

But what if the Breakthrough Boys are right – someday there will be a grand breakthrough and everyone will want fuel cells based on algae, or something. Then all those wind turbines and solar panels would become obselete. Wouldn’t that be awful? No it wouldn’t. We need to save ourselves from carbon right now. If we eventually get a pony for Christmas, fine. Developing yet another new industry will be good for the economy.

At the end you say
“I’m not against action but…”
That seems to be the essence of your position. Something will go wrong, so don’t even try to do nearly enough. I am sure you are able to make your concerns more concrete and quantitive, and one more time I suggest that you join <a href="http://www.realclimate.org/index.php/archives/2012/08/unforced-varations-aug-2012/comment-page-11/"this discussion. Meanwhile, your apparently small concern over CO2 Onward and Upward, vs your concern over possible market inefficiencies in the new technology adoption process, will have to remain a point of disagreement.

Pete,
The issues are quantitative and my views are my personal judments on them. I don’t expect that everyone would agree and I know that I cannot prove my point in a web discussion. I can only say that I try to tell honestly what I believe based on my 30 year experience in doing and managing energy research at a government research institute and at an university.

I do have trust in my own judgment but others may make up their minds on what they think. None of the counter argument that I have read here is new to me and I have taken them into account in my judments. It has been important for the discussion that they have been brought up because they have given me the opportunity to explain better what I think. This not perhaps the rigth place to continue further on these issues.

Pekka Pirilä,
I will share with you a piece of learning from my own experience. There are many levels of the understanding that constitute ‘knowledge’ and a whole lot more that fall well short of what we would rightly call ‘knowledge’.
‘Knowledge’ is not simply a matter of knowing, or even knowing well. The what of ‘knowledge’ is never independent of how it is known, why it is known and even where and when it was known.
To assert the answer to, say, the Schleswig-Holstein question is ‘halve Schleswig’ may be correct but unless this what is accompanied by the how, why when & where it does not constitute ‘knowledge’ and will likely lead to conflict, war even and perhaps more than one war.
I say this because one common symptom that accompanies incomplete ‘knowledge’ is an inability to explain to others what that ‘knowledge’ is. Indeed, such a situation strongly suggests that the holder of this ‘knowledge’ cannot even explain it to him/herself. And if that is so, we are into intuitive understanding, gut feelings and irrationality.

You say here “The issues are quantitative” which is a good sign but then offer no quantitative evidence. In fact, except for your “30 year experience in doing & managing” research in the subject, providing some sort of ‘authority’, you offer no evidence at all, nothing to allow your assertions here to be assessed. And following all our comments presented in this thread contrary to your own, you now say of them “I have (already) taken into account in my judgements,” and “This not perhaps the rigth place to continue further on these issues.”

If your intention for being here was to impart the wisdom of you 30 years experience, I would strongly suggest you have singularly failed in your intent.

Al Rodger,
In web discussion some comments are informative to a group of people and irritating to another group. From the first comments it has been obvious that we two just irritate each other and we hardly can change that except by not caring what the other is writing, perhaps not even reading that.

Neither of us knows what the others are thinking. Perhaps there are people who get some ideas from my texts and study them further and finally learn something – not necessarily agreeing then with what I said.

I told about my background not to claim any authority based on that (that would be futile anyway) but to explain why I have written in the way I have written. That again may or may not be helpful for understanding.

Net discussions are always very narrow. Sometimes the writer has nothing more in his mind, sometimes he tries to make a point hoping that the readers can put the comment in right settings. Possible further discussion is likely to provide some help in that as I think has happened with some readers of my comments.

The spectrum of opinions is not black and white. That applies also to people who agree basically on that the global warming is a serious issue and who have spent considerable and honest effort in finding out how we should react to it. It’s right to argue for what each one of us considers right but ridiculing those whose views differ is not right – except when the others are clearly not honest and sincere. “Open Mind” should refer to the tolerant attitude in this sense.

AI Roger complains about your communication. If he is justified, then it is not because “Neither of us knows what the others are thinking.” Rather, he doesn’t know what you’re thinking because you haven’t communicated it clearly. Appealing to different perspectives and some vague uncertainty in internet communication is a cop-out.

There are many reasons others might not agree with you. But if others don’t comprehend you, it’s not their fault — it’s yours.]

You may have noted that I actually went further in my previous comment than Tamino suggests. Tamino says I accuse you of not communicating clearly, that you do not fully explain what you are talking about. In truth, I went one step further suggesting that this poor communication is a symptom of you yourself not truly knowing what you are talking about. That is strong stuff.

Let me share an incident with you. A wise old professor once refused to accept an unsolicited thesis from me unless it was written on a single side of A4. The thesis was rather longer than that and I was a little shocked at the prospect of reducing its length. He went on to say that although a short thesis would be good for him, a time-strapped academic, it would be a greater benefit to me. He insisted that if I couldn’t rewrite the essence of my thesis onto a single side of A4, I obviously hadn’t truly grasped what the thesis was all about. This is a lesson that I (eventually) embraced wholeheartedly.

You are saying that contrary opinions will not be reconciled here. I would say that contrary opinion may persist but that it will be better defined by the process. But this requires contrary opinions presented here to be understandable by both sides.

You say “Net discussions are always very narrow.” (although you may be meaning ‘shallow’). I say that, of the comments you have posted in this thread, the longest one (at 647 words) would overflow a single side of A4. So there is scope here for any well-formed thesis to be presented, allowing continuing discussion to develop into narrower areas of dispute or interest.

Finally, you object to ridicule. My use of such may be because I object to encountering the ridiculous (although my objections will be heightened by conclusions presented which are at variance to my own views).

I’ve been thinking about 1 deg C shift in average temperature, and it for some reason, just didn’t appear to be alarming. But I think I was wrong thinking that (and I guess many just don’t realize this). It was short, not even very strong heat wave we experienced where I do live. But daily temps just went from 32 C (still OK), 33 C (rather uncomfortable), 33 C, 34 (quite uncomfortable) to 35 (uncomfortable) to 36 (very uncomfortable). Now, with just 1 deg of warming, same heat wave would be 33 C (rather uncomfortable), 2 days of 34 C (quite uncomfortable), 35 (uncomfortable), 36 (very uncomfortable) and 37 (really uncomfortable). So the collective level of being uncomfortable (scientist would measure stress levels to plants, animals, etc.) is quite big even for low increases in average temp.
I think more effort should be done to explain what these increases mean to plants and animals (including humans), to energy consumption (more refrigerating) and prices. It is a simplistic view, but I do think many people will be able to understand what 1 deg (yet alone 2, 3, 4 or more) warming actually means for their well being.

Solar electric panels can meet electricity demand on any scale, from a single home to a large city. There is plenty of energy in the sunlight shining on all parts of our nation to generate the electricity we need. For example, with today’s commercial systems, the solar energy resource in a 100-by-100-mile area of Nevada could supply the United States with all of its electricity“

That’s not Horatio’s claim or the claim of some self-proclaimed “expert” on the internet (you know the type, the ones who won’t/don’t provide any hard numbers or other evidence to support their claims but simply want you to accept their claims {opinions, basically} because they “have spent 30 years doing energy research”)

The above statement comes from a publication “Produced for the U.S. Department of Energy
by the National Renewable Energy Laboratory, a DOE national laboratory”

As far as cost, even if one assumes an installed cost of $0.20 (20 cents) per KWh (see the above ‘Energy Potential’ link) the US could install the solar capacity needed for ALL its current electrical use (about 4 trillion KWh) for about $800 billion.

That may seem like a lot, but not when compared to the YEARLY expenditures of the US government (among other things, to keep the oil flowing from the Middle east and elsewhere). As a comparison, revamping the infrastructure in the US would cost an estimated $2 trillion.

And the above solar system would ensure energy independence for US electrical needs for the life of the system (several decades).

It could be further scaled up to provide other energy needs as well (transportation, etc). And the above system is purely solar (does not include the potential from wind, for example) and does not even include the very large potential for individual-home solar systems.

The issue is clearly not that “we can’t do it” or that “it will put us all in the poor house” or that it will have “unknowable unintended consequences”.

The US government could certainly fund this as public works project if it wanted to, thereby boosting the economy and creating jobs. And actually, many large public works projects (interstate highway system in US, Hoover Dam, etc) end up paying for themselves many times over in the long run.

And there is no reason that it could not be done effectively, efficiently and with little corruption (eg, by having several independent groups — ie, outside the government — monitoring the money expenditure and work).

There are basically two reasons this is NOT being done.

The first is that the upfront cost is prohibitive to private industry, but as mentioned above, that issue is essentially a non-issue if one makes it a government funded public works project.

Second, (and here’s the showstopper) there are corporate special interests (fossil fuels and others) who don’t want this done because it would seriously cut into their bottom line.

And, of course, there are the individual naysayers (who post on blogs and write newspaper articles, etc) who (wittingly or unwittingly) act as cheerleaders for the special interests.

If America had listened to the naysayers (“we can’t do it” , “it will cost too much”, “we can’t foresee the unintended consequences”) back in the 60’s, we would never have put a man on the moon.

Your figures don’t quite multiply correctly. Taking your figures I see that we use 4 TWh/year. It costs $.20/kWh to set up solar panels. Ergo, it costs $800G/year to power entirely off solar. You forgot the per-year bit.

It is “Installed cost”, the “upfront capital investment” which comprises the vast majority of the cost for a solar energy system (other than a relatively small amount for maintenance). Unlike with fossil fuel or even nuclear electric production , the solar “fuel” is free.

The estimated kilowatt-hour rates assigned to solar energy are not based on the cost of electricity generation, they are based on the cost of the investment capital and the requirement to earn a return on investment, or pay back the loan for the investment. Remember, the solar fuel is free.

To see where the estimated cost of solar used above (0.20 per KWH installed) came from, see the graph at the bottom of the “Energy Potential” page.

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